Determine safety and tolerability of intravenous infusion of JX-594 followed by intratumoral injections with JX-594 prior to standard sorafenib therapy [ Time Frame: Safety evaluations through 28 days after last dose of JX-594 ]

Adverse events will be collected and assessed to assess safety and tolerability through 28 days after last dose of JX-594 (or until all events considered probably or possibly related to JX-594 have resolved, stabilized, or returned to baseline status).

Secondary Outcome Measures:

Determine Disease Control Rate (DCR) at 12 weeks [ Time Frame: Disease control and response assessment at 12 weeks from first JX-594 dose ]

1e9 pfu (plaque-forming units) total JX-594 dose on each of up to four (4) JX-594 treatment days. Sorafenib is initiated after 3 JX-594 treatments and briefly interrupted if an optional 4th JX-594 treatment is given.

Drug: JX-594 followed by sorafenib

Patients will receive a total dose of 1e9 per treatment starting with one IV dose on Day 1 and injected intratumorally in 1-5 intrahepatic tumors on Day 8 and 22. Starting on Day 25 (3 days after the final JX-594 dose) patients will initiate oral sorafenib therapy twice daily according to standard approved guidelines. An optional maintenance JX-594 dose may be given intratumorally at Week 12 (sorafenib briefly interrupted).

Sorafenib naive or refractory to sorafenib therapy Tumor Status: At least one intrahepatic tumor, and at least ≥50% of the total intrahepatic viable tumor mass, measurable by CT and injectable under imaging-guidance (note: injected and/or viable tumors must be previously untreated or ≥20% increase in size since preceding local-regional treatment).

Use of the following anti-viral agents: ribavirin, adefovir, cidofovir (within 7 days prior to the first treatment), and PEG-IFN (within 14 days prior to the first treatment).

Patients with household contacts who meet any of these criteria unless alternate living arrangements can be made during the patient's active dosing period and for 7 days following the last dose of study medication:

Pregnant or nursing an infant

Children < 12 months old

History of exfoliative skin condition that at some stage has required systemic therapy

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Please refer to this study by its ClinicalTrials.gov identifier: NCT01171651